Обучение чтению литературы на английском языке по специальности «Прикладная математика»
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Тематика:
Английский язык
Год издания: 2015
Кол-во страниц: 48
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Учебное пособие
Уровень образования:
ВО - Бакалавриат
ISBN: 978-5-7038-4198-3
Артикул: 840473.01.99
Учебное пособие состоит из трех уроков и содержит современные неадаптированные тексты, заимствованные из оригинальных источников, о сущности прикладной математики как науки и ее связях с другими науками. Каждый из уроков включает базовый текст А, упражнения на контроль понимания текстов, подбор активной лексики, перевод с русского на английский язык, умение читать математические формулы, а также дополнительные тексты
для различных видов работ с ними. Грамматические упражнения стимулируют повторение наиболее сложных грамматических конструкций. В Приложении приведен перечень основных математических символов и формул, а также даны варианты правильного их прочтения на английском языке. Для студентов старших курсов факультета «Фундаментальные науки», обучающихся по специальности «Прикладная математика».
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- ВО - Бакалавриат
- 01.03.04: Прикладная математика
- 02.03.02: Фундаментальная информатика и информационные технологии
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Московский государственный технический университет имени Н.Э. Баумана О.Д. Дикова, Е.А. Юдачева Обучение чтению литературы на английском языке по специальности «Прикладная математика» Учебное пособие
УДК 802.0 ББК 81.2 Англ-923 Д45 Издание доступно в электронном виде на портале ebooks.bmstu.ru по адресу: http://ebooks.bmstu.ru/catalog/238/book1233.html Факультет «Лингвистика» Кафедра «Английский язык для приборостроительных специальностей» Рекомендовано Редакционно-издательским советом МГТУ им. Н.Э. Баумана в качестве учебного пособия Дикова, О. Д. Обучение чтению литературы на английском языке по специальности «Прикладная математика» : учебное пособие / О. Д. Дикова, Е. А. Юдачева. — Москва : Издательство МГТУ им. Н. Э. Баумана, 2015. — 47, [1] с. ISBN 978-5-7038-4198-3 Учебное пособие состоит из трех уроков и содержит современные неадаптированные тексты, заимствованные из оригинальных источников, о сущности прикладной математики как науки и ее связях с другими науками. Каждый из уроков включает базовый текст А, упражнения на контроль понимания текстов, подбор активной лексики, перевод с русского на английский язык, умение читать математические формулы, а также дополнительные тексты для различных видов работ с ними. Грамматические упражнения стимулируют повторение наиболее сложных грамматических конструкций. В Приложении приведен перечень основных математических символов и формул, а также даны варианты правильного их прочтения на английском языке. Для студентов старших курсов факультета «Фундаментальные науки», обучающихся по специальности «Прикладная математика». УДК 802.0 ББК 81.2 Англ-923 МГТУ им. Н.Э. Баумана, 2015 Оформление. Издательство ISBN 978-5-7038-4198-3 МГТУ им. Н.Э. Баумана, 2015 Д45
ПРЕДИСЛОВИЕ Целью учебного пособия является развитие у студентов старших курсов, обучающихся по специальности «Прикладная математика», навыков работы с оригинальной научной литературой на английском языке, а также точного понимания и грамотного перевода текстов, ведения беседы по основным темам, затронутым в пособии. Задания по переводу с русского языка на английский направлены на повторение и закрепление терминологии по специальности, на использование необходимого грамматического аппара- та. Задания на прочтение математических формул позволят студентам получить достаточный навык изложения материала, содержащего математический аппарат, на английском языке. Грамматические упражнения направлены на повторение наиболее сложных конструкций английского языка. Владение терминологией по изучаемой специальности и языковыми оборотами английского языка, навыки понимания и перевода оригинальной литературы позволят студентам легче ориентироваться в потоке публикаций по специальности на английском языке, определять степень важности получаемой информации для собственной сферы деятельности, принимать участие в обсуждении профессиональных вопросов с зарубежными коллегами.
Unit 1 Texts: A. Pure and Applied Mathematics B. Why is the World Mathematical? C. Mathematics and Physics D. Revolution in Mathematics E. “Queen of Sciences” F. Experimental Mathematics Preliminary exercises I. Translate the following words and determine what part of speech they are. Explain your opinion. Find them in the text: National, international, nation, nationality, nationalism, nationalist, nationally; discuss, discusser, discussible, discussion; approximately, approximation, approximate; solve, solvent, solvable, solver; application, applicator, applicant, apply, appliancy, applicability, applied, appliance; extremely, extreme, extremeness, extremism, extremist, extremity; intractable, tract, tractable, tractate; essential, essence, essentially, essay; heavily, heavy, heaviness; mathematicians, mathematics, mathematical, math; probabilists, probable, probability; correctly, correct, correction, incorrect, incorrectly, correctness; joining, join, joint, jointless, jointly, joined; partition, part, particle, partial, partner, partly; loft, loftiness, loftily, lofty. II. Read Text A and find equivalent phrases in the right-hand column. Find them in the text: 1) строгость и доказательства a) solvable problem
2) начальные и граничные значения b) sloppy crackpot 3) теоретическая и прикладная математика отдаляются друг от друга c) to immerse oneself completely in the subject 4) глубокое понимание предмета d) joining of hands of people 5) индуктивный метод e) initial and boundary values 6) разрешимая задача f) living and breathing the subject 7) полностью погрузиться в тему g) pure and applied mathematics are drifting apart 8) необходимые качества h) inductive method 9) объединенные усилия людей i) rigor and proofs 10) неграмотный чудак j) requisite qualities III. Memorize the following basic vocabulary and terminology to Text A: pure mathematics — чистая математика applied mathematics — прикладная математика boundary value — граничное значение boundary value problem — краевая задача approximate solution — приближённое решение exact problem — строгая задача solvable problem — разрешимая задача intractable problem — трудноразрешимая задача initial value problem — задача Коши, задача с начальными условиями recognize the need — признавать необходимость Text A Pure and Applied Mathematics Toward the end of the recent International Congress of Mathematicians in Madrid, there was a discussion about whether pure and applied mathematics are drifting apart. The majority of the audience was pure mathematicians. So perhaps it would be helpful to ask, what is applied mathematics? A very good answer was provided by Kurt Friedrichs, who distinguished himself in both pure and applied mathematics, “Applied math
ematics consists in solving exact problems approximately and approximate problems exactly.” Initial and boundary value problems associated with the Navier-Stokes equations are an example of problems that are extremely difficult to solve exactly and where approximate solutions are looked for. Hence computing is an important part of applied mathematics. The Bhatnagar Gross-Krook equation in kinetic theory and plasma physics is an example of a solvable problem that approximates an intractable one. Some mathematicians believe that pure mathematics is a branch of applied mathematics. Some of the greatest mathematicians of the past — Newton, Euler, Lagrange, Gauss, and Riemann — and more recently Hilbert, Weyl, Wiener, von Neumann, and Kolmogorov did both pure and applied mathematics. There was the opinion that proofs are essential in pure math, but they are essential in applied math too, except that the path one takes is rather different. Applied math relies heavily on the inductive method, as opposed to the deductive method preferred by pure mathematicians. In pure mathematics the emphasis is on rigor. However, ideas are far more important. Ideas come from intuition, of course, which in turn comes from living and breathing the subject. Some of the scientists are quite right in insisting that even applied mathematicians need basic training in mathematics. One must also immerse oneself completely in the subject to which one wants to apply mathematics. It is by gaining a thorough understanding of the problems arising in the subject one develops a feeling for it, and with it, intuition. In applied mathematics the emphasis on rigor and proof must come at the appropriate stage. Let us consider an example. Feynman had great intuition but didn’t care much for rigor or proofs. He says in one of his autobiographical writings that once he used to talk to William Feller and Mark Kac, the famous probabilists. It is a happy circumstance, for science in general and mathematics in particular, that Feller and Kac didn’t dismiss Feynman as a sloppy crackpot but instead patiently listened to him. Thus the great Feynman-Kac formula was born. The moral, I think, is that pure mathematicians, while insisting correctly on rigor and proofs, must be patient and show some respect toward intuition born out of a deep knowledge of a subject. Attitudes like “Applied mathematics is bad mathematics” are shortsighted. For their part, applied mathematicians, while using intuition as their guide, must recognize the need for and the importance of proofs. On the other hand, it is
rare that a single individual embodies all the requisite qualities to a high degree. So often what is needed is a joining of hands of people with disparate abilities, strengths, and points of view rather than a separation or drifting apart. (3 253) Task 1. Answer the following questions. 1. What was one of the questions discussed at the recent International Congress of Mathematicians in Madrid? 2. How did Kurt Friedrichs define the difference between pure and applied mathematics? What example could prove his point? 3. What does applied mathematics require besides basic training in mathematics? 4. Thanks to what circumstances was the famous Fayman-Kac formula born? What is proved by that fact? 5. What is the source of intuition? 6. Why is the joining of hands of all mathematicians necessary in dealing with problems of mathematics? Task 2. Translate the following sentences into English. 1. Прикладная математика состоит в приближенном решении точных задач и точном решении приближенных. 2. Существует мнение, что доказательства очень важны в теоретической математике. 3. Только в результате глубокого понимания проблем, возникающих при рассмотрении конкретной темы, у человека развивается его тонкое восприятие, и с ним, интуиция. 4. Те, кто, занимаясь прикладной математикой, руководствуется интуицией, должны в то же время осознавать необходимость доказательств и их важность. Task 3. Read the following expressions, consulting the SUPPLEMENT. 1 3 8 ; 0.12; 9.43. 2x2 + 7x = 0; 5 10a – 3 = 2; 2x + 3 = 20 9 x ; 3 2 2 11x = 3 + x; K = 2 1 1 2 T R N R , 4 4 2 2 a – b a – b = 2 a + 2 b .
log m N = logN m ; 2sin α cos β = sin (α + β) + sin (α – β); 3 5 dx x ; 2 2 a a a – x dx; 2 2 sin cos 1 π x dx x . Grammar Revision Grammar task 1. Find the passive constructions in Text A and explain them. Grammar task 2. Translate the following sentences into Russian paying attention to the passive constructions. 1. The question of the laws of resistance in circuits may now be turned to. 2. Many materials now commonly used were not even thought of forty years ago. 3. This result was aimed at. 4. Mathematics, astronomy and physics were the first sciences to get organized and defined. 5. The speed with which arithmetic operations are performed is affected by a number of factors. 6. Questions can be asked and answered, but unfortunately the questions asked and those answered are frequently not the same. 7. These problems were being discussed by physicists for many years. 8. The equipment was sent for. 9. The force was acted upon. 10. Advantage was taken of this fact. 11. Use is being made of the new technique developed by the young engineer. 12. Care should be taken of the exact following the instructions. 13. This question was very important but not paid due attention to. 14. The weak points in the thesis were not taken notice of. 15. The young man left the city and was lost sight of. 16. Materials can be classed in three groups according to their electrical properties — conductors, semiconductors and insulators. 17. The results of the Dubna physicist research work are made good use of in such fields as biology, medicine, geology and science of metals.
18. An atom of any substance may be represented by a central core having a positive charge and surrounded by orbiting electrons, each having a negative charge. 19. Granules cannot be obtained from such metals. 20. The book was terribly bad; it was just a chance that it got published. Supplementary reading tasks Read and translate Text B without a dictionary Text B Why is the World Mathematical? This reflection on the symmetries behind the laws of nature also tells us why mathematics is so useful in practice. Mathematics is simply the catalogue of all possible patterns. Some of those patterns are especially attractive and are studied or used for decorative purposes; others are patterns in time or in chains of logic. Some are described solely in abstract terms, while others can be drawn on paper or carved in stone. Viewed in this way, it is inevitable that the world is described by mathematics. We could not exist in a universe in which there was neither pattern nor order. The description of that order (and all the other sorts that we can imagine) is what we call mathematics. Yet, although the fact that mathematics describes the world is not a mystery, the exceptional utility of mathematics is. It could have been that the patterns behind the world were of such complexity that no simple algorithms could approximate them. Such a universe would “be” mathematical, but we would not find mathematics terribly useful. We could prove “existence” theorems about what structures exist, but we would be unable to predict the future using mathematics in the way that NASA’s mission control does. Seen in this light, we recognize that the great mystery about mathematics and the world is that such simple mathematics is so farreaching. Very simple patterns, described by mathematics that is easily within our grasp, allow us to explain and understand a huge part of the universe and the happenings within it. (1520)
Read Text C and give a short summary. Text C Mathematics and Physics The traditional view is that mathematics and physics are quite different. Physics describes the universe and depends on experiment and observation. The particular laws that govern our universe — whether Newton’s laws of motion or the Standard Model of particle physics — must be determined empirically and then asserted like axioms that cannot be logically proved, merely verified. Mathematics, in contrast, is somehow independent of the universe. Results and theorems, such as the properties of the integers and real numbers, do not depend in any way on the particular nature of reality in which we find ourselves. Mathematical truths would be true in any universe. Yet both fields are similar. In physics and indeed in science generally, scientists compress their experimental observations into scientific laws. They then show how their observations can be deduced from these laws. In mathematics, too, something like this happens — mathematicians compress their computational experiments into mathematical axioms, and they then show how to deduce theorems from these axioms. If Hilbert had been right, mathematics would be a closed system, without room for new ideas. There would be a static, closed theory of everything for all of mathematics, and this would be like a dictatorship. In fact, for mathematics to progress you actually need new ideas and plenty of room for creativity. It does not suffice to grind away, mechanically deducing all the possible consequences of a fixed number of basic principles. An open system is much more preferable. Rigid, authoritarian ways of thinking are ineffective. Another person who thought mathematics is like physics was Imre Lakatos, who left Hungary in 1956 and later worked on philosophy of science in England. There Lakatos came up with a great word, “quasiempirical,” which means that even though there are no true experiments that can be carried out in mathematics, something similar does take place. For example, the Goldbach conjecture states that any even number greater than 2 can be expressed as the sum of two prime numbers. This conjecture was arrived at experimentally, by noting empirically that it was true for every even number that anyone cared to examine. The conjecture has not yet been proved, but it has been verified